Abstract
Archaeologists have often used their “eye” to interpret spatial patterns within cemetery sites. In this article, we will use Ripley’s K-function analysis to determine the proximity of statistically significant clusters within four early Anglo-Saxon cemetery sites: Wakerley, Norton, Berinsfield, and Lechlade. Using spatial and statistical methods supported by ArcGIS 10 we will explore the kernel density estimates of graves at the point of significance to discuss the organization of cemeteries as part of their chronological and social development. As a result of this investigation we will conclude that these sites were not organized into small clusters of nuclear family graves but large plots that contained the remains of varied, multivocational households.
Introduction
Early Anglo-Saxon cemeteries have been studied by antiquarians and archaeologists since the middle of the 19th century (Lucy, 2000). One of the characteristics that makes these sites so attractive for investigation is the presence of different types of grave-goods; swords, spears, brooches, pins, buckles, and knives, which allow a few burials to be considered in great detail. As a result many archaeological studies have focused on this martial culture to ask questions about the underlying organization of early medieval society (Härke, 1992; Sayer, 2009; Stoodley, 1999). However, it is also necessary to understand the organization of cemetery space because it is with this detailed contextual evidence that it might be possible to move beyond sites and objects to understand the lives past people led. The scope of cemetery investigation has transformed with the introduction of statistical and computer analytical methodologies, but this type of analysis has not always been received positively and many excavators still rely on their “eye” to understand patterns and divisions within funerary space.
Archaeology data is often fragmentary but it is inherently multiscalar operating from a regional or macroscale to the object or microscale. Excavation data is static, heterogenous, and composed of boundaries which mean multiscalar statistics like Ripley's K-function can be powerful ways to investigate complex problems. Situated within Geographic Information Systems (GIS) analytical technologies, statistics can become heuristic tools to make inferences about past human behaviors based on analytical processes that can test spatial patterns––clusters or aggregate patterning––against a null hypothesis. What this means is that by using GIS imbedded statistics it is possible to investigate more highly complex spatial patterning than would be possible with traditional static approaches.
In this study, we will investigate four cemeteries which date to the sixth century or to the sixth and seventh centuries AD: Wakerly, Norton, Berinsfield, and Lechlaide. At these sites, as at many similar early Anglo-Saxon cemeteries, archaeologists have visually identified clusters or plots of graves and attributed them to social groups, families, households, and communities. To investigate these observations we will use ArcGIS 10 to carry out a statistical analysis of grave plots using Ripley’s K-function analysis. However, Ripley’s K-function does not visually illustrate this clustering so we will support this study with kernel density estimation to show any intentional structure within the cemetery organization. We demonstrate that GIS data and software for processing spatial patterns augmented with the powerful statistical method in Ripley’s K-function is a powerful tool for identifying significant spatial patterns that improve understanding of the statistical and physical reasoning behind the spatial patterns of early Anglo-Saxon cemeteries.
Computer Application, Statistical Proof, and Cemetery Analysis
The application of computer analysis to archaeological sites is not new. Indeed, GIS and computer analysis are the main focus of research communities like Computer Applications in Archaeology, who hold an annual international conference. The statistical analysis of cemeteries is also not new, but appears only rarely in CAA’s proceedings, possibly because it has had a very mixed reception from scholars who are less mathematically and digitally literate. However, the conjunction of GIS and statistics enhances the role of each with respect to the analysis and interpretation of spatial patterns, and has been a major driver of GIS development which originated as a means to visualize the spatial distribution and analysis of data. The enhancement of statistical measurement from individual or ad hoc relationships to the spatial distribution of measurements opens new vistas for the analysis of the spatial record of human agency in a variety of landscapes, including cemeteries.
In the 1970s, and based on a long history of spatial analysis in social anthropology, Binford pointed out that archaeological sites are often the product of human agency and social decisions and so should contain spatial structuring which can be investigated accordingly (Binford, 1971). Similarly, Tainter (1975, 1977) applied statistical analysis to the problem of understanding social complexity from cemetery data. He used polythetic-agglomerative cluster analyses, or average-linkage analyses, to investigate the homogeneity of burial assemblages dating between 150 BC and AD 400 from Klunk and Gibson mounds in the lower Illinois River valley. Tainter (1975) explored mathematical clustering in what he perceived to be the energy expenditure invested in individual inhumations so that he could rank certain types of burial together based on the amount of excess energy employed. He then used this data to attribute social hierarchies according to the amount of wastage in each group. Working on early Anglo-Saxon cemeteries Pader (1980, 1982) also took a mathematical model for grouping similarities in grave-good assemblages together. She used a multivariate analysis which considered different objects alongside body position, age and gender differences in burial, and then analyzed that information alongside the spatial proximity of graves. She was trying to look, not at vertical hierarchies as Tainter had, but at how horizontal social factors such as symbolism, age, and gender affected funerary remains.
Tainter and Pader were working in different theoretical traditions, and perhaps unsurprisingly came to different conclusions about the viability of their methods. For example Tainter (1975) indicated that minor changes in grave-goods did not constitute viable differences from which to infer social divisions. Whereas Pader (1982) suggested that it was the minute changes in combinations of different characteristics which could be used as an indicator of social divisions made in cemetery spaces. This, however, was not their most significant problem, both studies were simply too opaque and driven by artificial numerical divisions in the cemetery data dependent on underlying user decisions that were not visible to traditional analysis. As a result one “post-mortem” of Tainters work suggests that his: “most glaring [fault] is the reductionist and scientific fallacy of representing a society as a number” (Parker Pearson, 1999, p. 75).
Contemporary proponents of spatial analysis could have been critical of Pader’s (1982) reliance on the immediate proximity of graves to interpret her statistical data. For example, Voorrips and O’Shea’s (1987) study of prehistoric sites in Russia neatly showed that nearest neighbor analysis had little significance for understanding cemetery organization where “Euclidean distance” may not be determined by social factors. However, they argue that spatial clustering and regularity in cemetery organization can be significant and maybe analyzed using spatial statistics (Voorrips & O’Shea, 1987). Equally Goldstein (1976, 1981) combined an examination of the material contents of graves with spatial origination using cluster analysis. She investigated two Mississippi valley cemeteries and looked at clustering in “elite” and “nonelite” graves, Goldstein concluded that:
The artefact-only analysis isolated individualised treatments, often divided on the basis of age and sex. The artefact-and-positioning groupings isolated the same most highly restrictive groupings . . . and reflected group membership over and above individualised treatments. These types are larger and less restrictive; they are not differentiated by age and sex, but represent group or perhaps kin affiliation. (Goldstein, 1981, pp. 65–66)
Voorrips, O’Shea, and Goldstein relied on the numerical identification of social elites and did not integrate chronology or social transformation into their statistical investigations, because of this and the variation evident between cemeteries, critiques have suggested that this “mirror of life” approach did not in fact represent the human experience (Barrett, 1990, 1994; Parker Pearson, 1999, pp. 83–87).
However, these criticisms focus in the interpretation of statistical information not on the methods used and numerical data is still often employed to understand human agency and the social aspects of burial practice, for example; the prevalence of weapons in graves (Härke, 1992) or the association of age categories and gendered objects (Huggett, 1996; Stoodley, 1999, 2000). GIS is also routinely engaged to understand ancient landscapes, or as a digital tool that can plot multiple grave variables spatially across large cemetery sites in hours rather than days (see Hakenbeck, 2006; Sayer, 2007; Šmejda, 2004). However, even though negative results can be quickly discarded, just like traditional paper methods the analysis of archaeological sites is only as good as the data available and the research questions posed.
The Spatial Analysis of Early Medieval Cemeteries
Since Hope-Taylor (1977, p. 262) incidentally noted that early Anglo-Saxon cemeteries seem to have either a single or multiple foci around which their graves cluster there have been a number of notable attempts to analyze spatial patterns within early Anglo-Saxon cemeteries. From Hawkes (1977) and Wells (1973) discredited endeavor to seasonally date graves based on a comparison of their orientation with that of the sunrise, to statistical methods like that of Pader (1982) and Ravn (2003). However, by far the most common presentation of this data is the analysis provided within published excavation reports.
In 1987, Evison published the results of her excavations at Dover Buckland and the resultant monograph set a standard for many future reports including some simple color plans and detailed artifact typologies, many like the analysis of knives remain the standard today (Evison, 1987, p. 113). The Dover Buckland account was part of a generation of excavation reports that included integrated plans of cemetery sites, and the relationships between graves. Before the 1970s excavators had not always though such things necessary (see Williams, 2009). Evison (1987) also provided an analysis of the spatial groups at Dover Buckland based on physical clustering according to a visual distribution of graves and the location of adults from different genders. Using this approach she inferred that the c.170 burials could be split up into 14 separate plots which were either nuclear family units, balanced between men, women, and children, or multiple units of a nuclear-family type. She went on to do the same style of investigation at Great Chesterford speculating, somewhat circularly, that clusters of graves implied the presence of large barrows, and that these intern were the tumuli under which nuclear-families were interred (Evison, 1994, p. 46).
It is probably not by accident that there were some striking similarity between Evison’s (1987) and Pader’s (1982) results. Both ended up dividing their respective cemeteries up into small groups with a handful of furnished graves within them, often to the exclusion of the physical clustering of graves themselves (see Figure 1). Similarly in 2003 Ravn published a comparison of a sample of sites across Northern Europe. Like Pader he used a complex system of multivariate statistics and correspondence analysis and applied them to his cemeteries to identify units of seriation or differences between groups of burials. One of his sites was early Anglo-Saxon Spong Hill where he was unable to show any spatial patterning demonstrating far more difference between burials than similarities (Ravn, 2003, pp. 99–129).

Grave plots at Westgarth Gardens and Norton. Westgarth Gardens (top) was interpreted by Pader (1982, Figure 7.2) as having six burial areas, and as the site only contained 66 burials these ended up as small “nuclear” units of men, women, and children. Norton was interpreted by Stoodley (2011, Figure 33.3) as consisting of four burial plots.
Multivariate investigations are an important way to reconstruct differences in society, but when indiscriminately applied to spatial distributions the analysis takes on two subtle assumptions: (1) that the open-grave plan view of a cemetery understood by an analyzing archaeologist is the same as the view experienced by its multiple users and (2) that individual differences in graves are significant and are remembered across generations of users. For example, Pader (1982) indicated that body position was a characteristic of individual inhumations which could be used to divide up groups of graves that were clustered together into smaller units. However, as individual burials were probably dug only rarely, and different funeral goers would have attended the burials of each individual, it is very possible that small variations like this are not easily transmitted between generations (Sayer, 2010). Both sociologists and anthropologists point out that each funeral is different because different people construct it and they bring different memories, values, and ideas to the event (Walter, 1994, pp. 156–157). When an early Anglo-Saxon cemetery was in use its graves were closed and the events of a funeral from half a century before may not be remembered or understood by a new funeral party. Especially if that party consisted of a mixture of people; those who had been to the earlier event and those who had not even been born and do not have a memory of it. Indeed, Evison and Pader, did not engage with the chronology of their grave clusters preferring instead to see interred nuclear families, consisting of adult males and females with their children. Unfortunately for us, past people did not die in fixed slices of time and fall into their graves as family units, rather a parent's children may have grown up to be adults themselves and it was probably their children who would have buried them in a community cemetery (Sayer, 2010).

Wakerley Grave Plots. Top: Kernel density plan of graves at 2 m which was significant in the Ripley’s K-function analysis. This plot shows three grave plots, an eastern, central, and a western plot. Below: Kernel density plot of the furnished burials at 2 m. When compared to the top image this suggests that the furnished burials formed clusters, or cores, within the larger cemetery plots.

Norton Grave Plots. Kernel density plan of graves at 6 m which was significant in the Ripley’s K-function analysis. This plot shows two noticeable grave clusters, a western plot and an eastern plot. They are separated by a 5 m wide gap in the cemetery that shows up as an empty strip down the middle of the cemetery.
Four Early Anglo-Saxon Cemeteries
We have chosen to investigate four early Anglo-Saxon cemeteries because they are all large sites with enough graves to constitute a statistical test. In the sixth century AD, graves rarely intercut, meaning that the people digging each new grave knew the position of the previous ones, so there must have been some marking of the graves and possible some organizational principles in operation within the cemetery. However, each of our sites looks physically different in plan so it is hoped that by comparing these four cemeteries we will be able to determine if the principles used in their organization were similar or varied from cemetery to cemetery and so between communities.
Wakerley
Wakerley early Anglo-Saxon cemetery is located in Northamptonshire, just two kilometres south of the village of Wakerley. The site consisted of 85 excavated skeletons in 72 graves and dates to the sixth century AD. The excavators Adams and Jackson (1988–1989, pp. 74–75) visually identified three major groups of burials in the cemetery: A western group, a center group, and an eastern group. There are physical differences in the graves: The western plot has the shallowest inhumations and the eastern group has the deepest inhumations ,and the highest density of burials.
Norton
The cemetery at Norton is located in north Cleveland, just to the north of Norton. It consisted of three cremations and 117 inhumation graves dating predominantly from the sixth century but with a small number of graves from the early seventh century. The site was excavated between 1983 and 1985 and is believed to be almost entirely complete because it is bounded on three sides: By the Hollow Way just to the north; to the south, by a series of Romano-British or Iron Age ditches; and by the slope down to the marshes of the Billingham Bottoms (river) to the east. Norton is a large Anglo-Saxon cemetery and the excavators suggested it was laid out in rows rather than plots, and these were divided into two visible halves by a gap, five metres wide, down the cemeteries central axis (Sherlock & Welch, 1992, p. 15). Stoodley (2011, p. 654) on the other hand identifies four plots in the site because he recognized a series of children’s graves positioned around an adult burial core in each plot. He suggests the smaller plots were shorter lived social groups (see Figure 1).
Berinsfield
Berinsfield early Anglo-Saxon cemetery is located in the Upper Thames valley, to the east of Berinsfield, Oxfordshire. Archaeological rescue excavation was carried out between 1974 and 1975. The excavation consisted of 100 grave cuts containing the remains of 114 burials and four cremations burials represented about two-thirds of the size of the original cemetery (Boyle, Dodd, Miles, & Mudd, 1995, pp. xvi–xviii). The graves date to between the mid-fifth and early-seventh centuries. Härke (1992, pp. 170–171) focused on an investigation of male weapon burials from which he suggested that Berinsfield was a polycentric site with three household units interring their dead in three different plots in the cemetery. Based on the female graves Stoodley (1999, p. 134) observed a similar pattern dividing them up into three groups. Williams (2006, pp. 46–62) also looked at Berinsfield and suggested that there may be three or four groups visible from the spatial clustering of brooches and weapons.
Lechlade
Lechlade early Anglo-Saxon cemetery is located in the Upper Thames Valley region to the north-west of Lechlade, Gloucestershire. Archaeological rescue excavation took place in the summer of 1985. The cemetery consisted of 219 inhumation graves in 199 grave cuts, as well as 29 cremations representing around three quarters or more of the original site (Boyle, Jennings, Miles, & Palmer, 1998, pp. xi–1). This site can be split into two phases, the late fifth and sixth century and the seventh century AD. In the first phase, Sayer (2007) visually identified three different plots within the cemetery based on the spatial distribution of graves and objects. The second phase in the seventh century sees the loose distribution of northwest–southeast oriented burials across the site (Boyle et al., 1998), and a new area of mixed orientation burials to the south of the sixth century site (Sayer, 2007).
Method
Preparing the Cemetery Data
Each early Anglo-Saxon grave is different which means it is often hard to see patterns for the detail; a situation that contributed to Ravn’s (2003) unsuccessful attempt to identify patterns at Spong Hill. Huggett (1996, p. 356) concurs and suggested that individual variations, like body position, were not significant universal characteristics being manipulated by the individual funerary party. Variations like these may have resulted from specific decisions rather than elements that resulted from the overall cemetery organization. Having said that, the burial of some individuals within a cemetery––community leaders, ritual specialists, or key family members––may have been expressed using the grave assemblages to convey messages, and this will influence how these individuals were subsequently remembered (Huggett, 1996; Sayer, 2009, 2010; Williams, 2006). For example a community leader may be buried in a group of former (and future) leaders at the heart of a larger burial plot and so furnished graves must be considered within the whole cemetery but also independently to unfurnished graves because they may have had a greater influence on how and where subsequent inhumations where interred. Equally the placement of sixth century graves is not affected by the location of seventh century graves so they should be removed from an analysis of sixth century burials. For this study, the early Anglo-Saxon burial tradition was considered to consist of two phases, the late fifth to sixth century and the seventh century (Geake, 1992; Sayer, 2010).
To incorporate this data into the investigation, a site plan was generated in AutoCAD with each grave layered individually by its grave number. This was imported into ArcGIS 10 and joined with an Excel database by an assigned grave number with grave attributes. The two attributes used in this study were: (1) the presence of a furnished grave which included as a minimum two brooches for women or multiple weapons for men (brooch and weapon sets have been identified as a significant indicator of social position used as a method of display in the early Anglo-Saxon funeral, Härke 1990; Shephard 1979; Stoodley 1999) and (2) chronology, labeled either sixth century or seventh century and based on the dates of grave-goods, stratigraphy, or visual devices like orientation that separated later graves from earlier graves (see Sayer, 2007).
Ripley’s K-function
Few studies have incorporated a Ripley’s K-function analysis (Ripley, 1976, 1977, 1981) for archaeological data (for artifact distribution see: Orton 2005; for site distribution see: Bevan & Conolly, 2006; Winter-Livneh, Svoray, & Gilead, 2010), and to date none have used this type of point-pattern analysis to consider grave distribution. In its most basic definition, Ripley’s K-function is a way to measure statistically significant clustering or aggregation and regularity or segregation of point data at multiple scales regardless of the shape of the area being studied (Conolly & Lake, 2006, p. 166). Archaeological data is inherently multiscalar and is composed of boundaries, which makes Ripley’s K-function well suited for this type of analysis. Although more intuitive and easier to interpret, nearest neighbor analysis was not considered for our data sets because increasing the nearest neighbor measurement to nth number of neighbors does not easily allow for statistical validation (Conolly & Lake 2006, p. 165; Hodder & Orton, 1976, p. 41;). Furthermore the size of the study area greatly influences the results (see: Bevan & Conolly, 2006, pp. 218–221; Conolly & Lake, 2006, pp. 164–166).
For the four cemetery data sets presented here and the sub-data sets of status and chronology, the Ripley’s K-function was used to evaluate if there were human decisions underlying grave placement. The ArcGIS 10 spatial statistic function Multi-Distance Spatial Cluster Analysis (Ripley's K-function) was applied to the data sets. The K-function is defined as:
Therefore, when L(d) < 0, it indicates regularity or segregation within the data set, L(d) =0 is spatial randomness, and L(d) >0 indicates clustering or aggregation within the data set (see Pelissier & Goreaud, 2001, p. 102). This analysis was run using Monte Carlo simulation in order to produce statistically significant results. Monte Carlo simulation randomly generates a distribution of points equal to the number of input points which creates the confidence intervals or envelopes according to the number of permutations (Winter-Livneh et al., 2010, p. 288). This means that when L(d) >0 falls above the high confidence intervals then there is statistically significant clustering and when L(d) <0 falls below the low confidence interval there is segregation of the data. For the purposes of our analysis 999 permutations were used to generate 95% confidence intervals. Edge effects were also accounted for using the Simulate Outer Boundary Values method available within the program because archaeological data are comprised of edges (e.g., excavation extents). Therefore each area being excavated is not assumed to be the full extent of the burials.
Originally this type of analysis was designed for data sets that were assumed to be homogeneous and isotropic (e.g., Euclidean or crow flies distances) but archaeological data sets are inherently heterogeneous or comprised of multiple underlying cultural processes (Orton, 2005, p. 5). Therefore, our analysis studied each site locally or at an intrasite scale in order to prevent the occurrence of heterogeneous environments and the data was split for each site into categories of social status and chronology based upon associated artifacts (which is also recommended by Bevan & Conolly, 2006).
Kernel Density Estimation
Finally, for our second analysis, we choose a more informal means in order to easily visualize and define the areas of clustering for the data. In order to spatially visualizes, the areas of point aggregation within each local or site scale a kernel density estimation analysis (after Silverman, 1986) was performed on the whole data set and the subcategories of social status and chronology. This type of analysis provides a way to interpret clusters within the data set and makes it more apparent to visualize where the “holes” or spaces are between these concentrations. It also allows for the comparison of different types of data within the same site at the same radius. Density analysis, also referred to as intensity analysis, looks at the how the frequency of distributions for point data changes over the study area (Conolly & Lake, 2006, pp. 173–174). Furthermore, as argued by Baxter and Beardah (1997, pp. 347, 351), this analysis provides a smoother visualization of the data, it does not depend on a starting point and it does not output clusters in spherical shapes which are not reflective of real-life distributions. Kernel density estimation in its formal definition “is a nonparametric technique in which a two-dimensional probability density function or the “kernel” is placed across the observed data points to create a smooth approximation of its distribution from the center of the point outwards” (Conolly & Lake, 2006, p. 175). ArcGIS 10 kernel density analysis was used and applies a quartic approximation of a Gaussian kernel that cannot be changed within the software. It does, however, allow for the search radius or the “kernel” to change. In order to study our data, the data sets were plotted at the statistically significant distance that the Ripley's K-function identified and at 5 and 10 m intervals so that clusters of graves could be seen on overlaid cemetery plans.
Results
Wakerley
Wakerley showed significant clustering for Ripley’s K-function analysis after 2 m (see Appendix A) the burials without a fully furnished grave (weapon or brooch sets) where more dispersed with significant clustering after 3.5 m. The furnished graves results showed statistically significant clustering after 2.5 m, although with only 28 graves this was not an ideal assessment. This result suggests that there are burial plots with an internal organization where the furnished burials are more concentrated within those plots than the unfurnished burials.
The Kernel density plot illustrates this clustering (Figure 2), where there are three dense areas of burial visible at 2 m, a large eastern and central cluster and less dense south western cluster. The plots themselves are visible where there are gaps,in shading that mark the absence of graves, in other words, the lightest sections within the shading mark the areas between these three plots. There is a single grave situated between the central and western plot that sits at the midpoint between the two clusters and was probably located in this “between” situation deliberately.
Norton
Norton showed significant clustering for Ripley’s K-function analysis after 6 m (see Appendix B). This cemetery has clusters of graves, but they are noticeably less dense than at other sites in this study and each cluster seemed to operate over a larger area. When plotted at 6 m the kernel density analysis indicates the presence of two large plots separated by the 5 m gap that was identified by the excavator (Figure 3). Norton, unlike Wakerley does not seem to have central clusters of furnished burials, or at least these cannot be shown using Ripley’s K-function. As a result this is a much more dispersed cemetery something which might explain Stoodley’s (2011) division of the site into four smaller units where the gaps between burials on the edges of the two large plots seemed to be more significant that they actually were. As at Wakerly there is a single grave that sits on or almost on, the dividing line between the two large plots.
Berinsfield
Berinsfield is a much more densely clustered cemetery than either Norton, or Wakerely, with the Ripley’s K-function analysis showing statistically significant clustering at 1.25 m (see Appendix C). Unfortunately there were too few furnished burials to provide a statistically significant analysis for status. The kernel density at 1.25 m illustrates the two groups of burials on the eastern edge of the site; however, the plot at 5 m (also a statistically significant point on the K-function graph) shows a single linear burial plot down the center of the site with three smaller clusters of burials to the east, south east, and south west. Nevertheless it is important to consider the contextual information in this interpretation because Berinsfield has a small number of seventh century burials interred in the middle of the site and these do not seem to respect the earlier, sixth century, funerary tradition. As a result it is important to remove these burials from the kernel density analysis to understand the plots which were developed during the first phase of this site (Figure 4). The adjusted kernel density plot shows two clusters of burials with a dividing line between them along an east west line. What is interesting about this division is that the majority of sixth century burials in the southern plot are buried on an east–west orientation, and the majority of those in the northern half are on a south–north orientation so the clustering of graves does not seem to have been the only strategy employed to divide these two groups (also see Sayer, 2010, pp. 72–73). In the sixth century, Berinsfield cemetery consists of two large clusters of graves, and within those clusters were further concentrations of burials within which were positioned the wealthier burials (located in the darker areas on Figure 4).

Berinsfield Grave Plots. Kernel density plan of graves at 5 m (left) which was significant in the Ripley’s K-function analysis. The graves clustered and 1.25 m but the patterns are visible at 5 m, even though all the graves seem to be connected. Kernel density plan of graves at 5 m with the seventh century burials removed (right) the site now looks to be separated into two halves with a distinctive gap between the two.
Lechlade
The graves at Lechade, like Berisnfield, are much denser than at Wakerley or Norton. The Ripley’s K-function analysis showed clustering at 0.75 m (see Appendix D). Like Berisfield it was also in use across two phases, the sixth and the seventh century, and inhumations from these two different periods seem to have had been treated in different ways. When plotted independently the sixth century burials show significant clustering at 0.75 m but the seventh century burials have the significant clustering at 8 m, a much more dispersed pattern reminiscent of Norton. This contrast is striking and as a result each phase must be considered separately.
Lechlade is in the Upper Thames valley, where wealthy burials are less common than in contemporary Kent for example. It is also not immediately obvious how the site is organized from the kernel density plot alone (plotted at the 5 m interval see Figure 5), however, both at Wakerley and Berinsfield it seemed that by using multiple characteristics; clustering and grave-goods (social status), or clustering and orientation, that the shape and location of the burial plots can be seen. In this case, like many contemporary cemeteries (Abingdon, Bargates, Broadstairs, and Dunstable; Härke, 1992, pp. 243–262), Lechlade seems to be focused on a Bronze Age Barrow and it is around this feature that the graves are most densely clustered. However, this “mass” of burials may itself be two clusters and the locations of the graves with grave-good strongly suggests that there are two separate groups of burial: a northern plot and a southern plot whose kernel density is masked by a series of inhumations placed around the bottom of, and in alignment with, the south-western edge of the barrow giving the false impression of a single grave plot. The eastern plot is testament to this type of underlying organization where a low density grave distribution, or an empty strip, separates the eastern burials from those in the west.

Lechlade Grave Plots. Kernel density plan of sixth century graves at 5 m (left) which was significant in the Ripley’s K-function analysis. The graves clustered and 0.75 m but patterns are visible at 5 m. This site seems to be divided up into three clusters; a northern cluster with a group of furnished burials, a southern cluster with a group of furnished burials, and an eastern cluster also with a small group of furnished burials. The seventh century burials are shown at 8 m (right) which was significant in the Ripley’s K-function analysis. This group is much more spread out around the cemetery.
Interestingly the seventh century phase of the site (showing statistical clustering at 8 m in Figure 5) also shows a similar pattern to the sixth century plot with higher concentrations of burials in the northern, southern, and eastern areas of the site. However, these are much more loosely spread around the cemetery, actually over 10 times less dense than in the sixth century, and strikingly they are predominantly interred on a northwest-southeast orientation with a noticeable extension to the boundaries of the site to the south. This is a change in the positioning, location, and orientation of graves within this site.
After the assessment of the data present at the four sites, we find that most of these sites have statistically significant clustering for p <.01. Another trend that these analyses show is that the clustering or aggregation continues as the scale increases or is linear in nature. According to Orton (2005, p. 7), when the output of the K-functions show a “strong aggregation at large scales for all the classes, a clear indication of spatial inhomogeneity [sic] in the data, and an indication that the space should be divided for finer-grained analysis.” Considering that archaeological data is inherently heterogeneous, this is hardly surprising. Although outside the scope of this article, additional analysis could be performed on the individual clusters that these data sets identified to further understand the heterogeneous nature of these plots. One way of doing this would be to use the output of the kernel density analysis at 5 m to distinguish where the clustering is taking place and select the points within these clusters for a Ripley K-function or break up the sites based on the main clusters identified visually (as recommend by Orton, 2005, p. 7).
Conclusion
In this investigation, we studied four early Anglo-Saxon cemeteries to explore the spatial distribution of graves on an intrasite scale and test the hypothesis that early Anglo-Saxons were buried in plots or clusters of graves within larger burial sites. The study of patterns within cemeteries is not a new topic of enquiry but has tended to produce distributions that describe small “nuclear” family type clusters, no matter how easily that sits on the physical cemetery layout. Using a Ripley’s K-function analysis we have been able to statistically test burial patterns in cemeteries. At our four sites it is apparent that clustering does occur but can manifest in a number of different ways; close groups of graves tightly knitted together like at Berinsfield or Leachlade, or as lose groups of graves up to 8 m apart as we saw at Norton. They can be visually identifiable units with the cemetery landscape, as at Wakerley, or they can require a little further analysis because they are hidden by later graves. What is apparent from this investigation is that cemetery data needs to be understood within its contextual setting. The phasing of a site is a good example of this contest, an investigation of grave clusters at Lechlade would have yielded little result without further knowledge of the cemetery chronology, changing burial practice, and the presence or absence of furnished and unfurnished graves.
Hope-Taylor (1977, p. 262) was correct; many early Anglo-Saxon cemeteries do have a multifocal organization. But the nature of that organization varies as much as every other aspect of early Anglo-Saxon burial practice. However, rather than many plots such as the three or four at Berinsfield (Härke, 1992; Stoodley, 1999; Williams, 2006) there are just two, equally Norton does not seem to have been organized around rows of graves, but two large dispersed burial plots containing a range of different burials; adults, children, unfurnished burials focused on an internal furnished cluster or dispersed around the plot. Sixth century Wakerley consisted of three similar plots as did Lechlade but with a dispersed seventh century burial tradition overlaying it. These large plots do not contain the remains of equally ranked members of a nuclear family units, but big, varied, multivocational households interring their dead in a specific place for a hundred years or more, and the study shows that they were actively planning the organization of their cemetery throughout its use.
As others have shown Ripley’s K-function can be successfully applied to archaeology to identify statistically significant clustering or regularity for different types of archaeological data. What we have demonstrated is that Ripley’s K-function works particularly well for cemetery analysis because it is a flexible mathematical function operating on multiple scales meaning that it is flexible enough to be applied to complex, heterogeneous, sites because human decisions and cultural values underlie that sites evolution. GIS data and software for processing spatial patterns augmented with the powerful statistical method in Ripley’s K-function is particularly good at producing a scale at which spatial patterns are significant and in combination with kernel density analysis and a detailed contextual consideration of archaeological sites, and this is a powerful tool for identifying spatial patterns and then for understanding them.
Footnotes
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Appendix D
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
